# Getting started¤

**floquet** is a python package for performing floquet simulations on quantum systems to identify nonlinear resonances.

## Installation¤

For now we support only installing directly from github

```
pip install git+https://github.com/dkweiss31/floquet
```

Requires Python 3.10+

## Example¤

Before jumping straight into the Floquet analysis, we first need to define our system Hamiltonian and the drive parameters. Here we take the example of a transmon and utilize the scubits library to help define the system Hamiltonian. Note however that the code accepts QuTiP `Qobj`

as input for the Hamiltonian.

```
num_states = 20
qubit_params = {"EJ": 20.0, "EC": 0.2, "ng": 0.25, "ncut": 41}
tmon = scq.Transmon(**qubit_params, truncated_dim=num_states)
hilbert_space = scq.HilbertSpace([tmon])
hilbert_space.generate_lookup()
evals = hilbert_space["evals"][0][0:num_states]
# Define the Hamiltonian of the transmon in its eigenbasis, in which H0 is diagonal
H0 = 2.0 * np.pi * qt.Qobj(np.diag(evals - evals[0]))
# Use this helper method to define the charge-number operator in the dressed eigenbasis
H1 = hilbert_space.op_in_dressed_eigenbasis(tmon.n_operator)
```

```
omega_d_values = 2.0 * np.pi * np.linspace(7.5, 10.0, 120)
```

```
import floquet as ft
state_indices = [0, 1] # get data for ground and first excited states
chi_ac_linspace = 2.0 * np.pi * np.linspace(0.0, 0.1, 59) # 100 MHz ac-Stark shift
chi_to_amp = ft.ChiacToAmp(H0, H1, state_indices, omega_d_values)
drive_amplitudes = chi_to_amp.amplitudes_for_omega_d(chi_ac_linspace)
```

`Model`

which specifies the model system
```
model = ft.Model(
H0, H1, omega_d_values=omega_d_values, drive_amplitudes=drive_amplitudes
)
```

`FloquetAnalysis`

class, and run the full Floquet simulation
```
options = ft.Options(num_cpus=6)
floquet_analysis = ft.FloquetAnalysis(model, state_indices=state_indices, options=options)
data_vals = floquet_analysis.run()
```

`data_vals`

is a dictionary containing all quantities computed during the call to `run()`

. This includes the overlap with the "ideal" displaced state, which can be plotted to reveal "scars" in the drive frequency and amplitude space where resonances occur. This part of the analysis is based on Xiao, Venkatraman et al, arXiv (2023), see Appendices I and J. Additionally we perform a so-called branch analysis to understand which states are responsible for ionization, based on Dumas et al, arXiv 2024. See the tutorial notebooks under Examples on the left for example applications of the analysis, how to plot and visualize the computed quantities, etc.
## Citation¤

If you found this package useful in academic work, please cite

```
@misc{floquet2024,
title = {Floquet: Identifying nonlinear resonances in quantum systems due to parametric drives},
author = {Daniel K. Weiss},
year = {2024},
howpublished = {\url{https://github.com/dkweiss31/floquet}}
}
```

Also please consider starring the project on github!